Question

convert the following Polar equation into rectangular.

r=3sec(theta)

Answer 1

hmmm, I keep on getting a horizontal line :|

Answer 2

but I guess that's it, anyhow, just change around the sec() for its cos() identity :)

Answer 3

a vertical line I meant

Answer 4

I am still really confused. =(

Answer 5

ok,
$$
sec(\theta)=\cfrac{1}{cos(\theta)}\\
so\\
3sec(\theta) = 3 \times \cfrac{1}{cos(\theta)} \implies \cfrac{3}{cos(\theta)}\\\\
$$

Answer 6

$$
so\\
r=\cfrac{3}{cos(\theta)}\\
\text{now divide both sides by "r", so}\\
1=\cfrac{3}{rcos(\theta)} \implies rcos(\theta)=\cfrac{3}{1}\\
\text{now keep in mind that } \color{blue}{x = rcos(\theta)}
$$

Answer 7

This is what I got so far, could you help me from here?

\[3\times \sqrt{y^2/x^2 +1}=\sqrt{x^2+y^2}\]

Answer 8

see above :)

now that's a vertical line :|

Answer 9

I am so sorry, I am really bad in pre-calculas....I am not getting how to simplify down my answer.

Answer 10

still confused?

Answer 11

yea I feel really stupid.

Answer 12

well if x = rcos(a); then from the above equations,
x=3
which is a vertical line

Answer 13

so they cancel out leaving only x=3? I get it now. Thank you so much for your help!!